The author considers the effect of resonance particles drifting under the influence of magnetic field inhomogeneity with a velocity close to the phase velocity of flute oscillations on those oscillations. He investigates the instability of these oscillations at densities below the critical density of the hydrodynamic flute instability Ra/d2 ≪ 1 (R – radius of curvature of the magnetic field lines, a – transverse dimension of the plasma, d – Debye radius).It is shown that, when resonance particles are present, the branch of oscillations with frequency (ω0 – ionic plasma frequency, ωc – ionic cyclotron frequency, k – transverse wave number) is always unstable. For an ion transverse velocity distribution function having the form of a δ-function with an admixture of hot ions, it is shown that the branch of oscillations with a frequency only slightly dependent on density and close to (v0 – mean ion velocity) is also unstable. Both instabilities also occur in the hydrodynamically stable case; i.e. when the magnetic field lines are convex with respect to the plasma.